[Gretl-users] Overview of nls

[Allin Cottrell]

On Thu, 29 Jun 2006, Ryan J. Pieszak wrote:

> In the documentation shown below (from the gretl-guide.pdf), 
> are the regression functions being passed in standard 
> functions?  How would I know what function to pass in?  My 
> assumption was that I could just pass in the data sets and 
> gretl would give back the parameters used to build the 
> function.

I'm not quite sure I understand the question but I'll try.
In gretl's NLS you, the user, have to specify the nonlinear 
function that you believe may be generating the data.  For 
example,

> nls C = alpha + beta * Y^gamma

is a nonlinear consumption function that William Greene put 
forward as a possible generalization of the "simple textbook" 
version

C = alpha + beta * Y

How do you come up with such functions?  Basically, either you 
find them suggested in the economics literature, or you invent 
them yourself based on your knowledge of general economic theory 
and your intuition.

There are some programs available (e.g. genetic algorithms) 
where you can throw in a dependent variable and a mess of 
independent variables, and ask the program to figure out how 
they are related, if at all.  Gretl's NLS is not like that: you 
supply a structure and gretl figures out the optimal parameter 
values.

> Also, it says that if the nonlinear function is a 
> generalization of a linear model, running the ols and passing 
> it's coefficient estimates in as the intial parameters would 
> be more accurate.  How do I know if the nonlinear function is 
> a generalization of a linear model?

That's really just a matter of mathematical perception.  In 
relation to Greene's function above, you can see that if gamma = 
1 it reduces to a linear relationship between C and Y, so we 
might try starting with gamma = 1.  In general, we ask: is there 
some parameter in this function such that, if we set it to 1 or 
0 or something, the function collapses to a linear one?

Allin Cottrell